Interactions of low molecular weight molecules with food are an integral part of food science. Among the most important interactions are those involving water with carbohydrates and proteins. This insertion also affects food components such as vitamins and enzymes. Equilibrium studies in the form of sorption isotherms are particularly useful for evaluating the thermodynamics of these interactions.
A sorption isotherm is essentially a set of data defining the relationship at a particular temperature between solute vapor pressure in the surroundings and solute content of the food at equilibrium. Most of the methods which are used to determine sorption isotherms are gravimetric (static methods) and are based upon equilibration of the sample over time at constant vapor pressure and temperature. These methods usually require long periods of time to achieve equilibrium, and require numerous repeated experiments at different vapor pressures to develop the full set of data constituting the isotherm.
Inverse gas chromatography (IGC) has also been used to determine sorption isotherms of food. The advantages of using this approach are that small samples of materials may be used, sorption data may be determined quickly, and the sensitivity of the method in the low vapor pressure region is very good. Inverse chromatography is a test method wherein a fluid or "mobile phase" bearing the solute is passed through the solid or stationary phase material to be studied. The properties of the stationary phase are deduced from observations of the solute content in the mobile phase leaving the solid. In inverse gas chromatography the mobile phase is a gas. The use of specific vapor detectors, such as thermal conductivity, flame ionization and mass spectrometry, greatly enhances the specificity and sensitivity of the method.
The inverse gas chromatography method is sensitive to the rate of sorption of water vapor and measures kinetic effects which tend to be obscured in the long term gravimetric method. Sorption can be controlled in an inverse gas chromatography experiment by varying the factors contributing to contact efficiency thereby producing insights into the structure of the solid phase and into non-equilibrium sorption rate. A study with the gravimetric method reveals that this static method may not yield a final equilibrium sorption value. Instead, the gravimetric method stops at a point where the rate of water vapor sorption to achieve the remaining sorption equilibrium differential has slowed down to the point where a gravimetric determination shows no measurable gain in weight, a function of the sensitivity of the method.
The two major types of inverse chromatography are frontal analysis and pulse (elution) analysis. In frontal inverse chromatography, the entire sample of solute is introduced continuously into the column. Frontal chromatography may be divided into sorption and desorption phases. When a constant supply of mobile phase with a defined single solute concentration is supplied to a column, there is an initial delay in transit because of solute sorption. This period of delay is followed by a period of increasing solute concentration in the stationary phase which produces a corresponding rise in solute concentration in the mobile phase leaving the column until both phases are saturated in equilibrium with the input concentration. Consequently the exit concentration reproduces the sorption isotherm for the range of the input partial pressure of the solute. The subsequent passage of pure mobile phase produces the desorption isotherm.
In elution chromatography, an initial concentration of solute is introduced into a column of sorbant followed by pure mobile phase. An individual component is eluted from the column as a distinct peak as a result of the selective retardation of that component by the stationary phase. The peak formed on exit has an area proportional to the injected mass and a retention time related to the partition coefficient of the equilibrium zone.
The frontal inverse chromatography sorption method provides satisfactory agreement with static or long term equilibrium studies but requires a series of maintained solute concentrations to cover the full sorption isotherm range. The longer equilibrium periods required in frontal inverse chromatography, as compared to elution inverse chromatography, also require more elaborate controls of the chromatographic conditions. The pulse or elution sorption chromatography method, although not as accurate as frontal chromatography, has the advantages of rapidity and simplicity.
The height of the peak in the detector response is related to the partial pressure of the solute at any time. The area of the peak is proportional to the amount of solute injected, whereas the so-called "pre-peak area", and other parameters derived from the detector response versus time, is related to the amount sorbed. Since the calculations for the above two methods assumes equilibrium conditions, the validity of the methods requires ideal conditions, where equilibration is rapid compared to transit time. In order to achieve these conditions, the common practice is to use low concentrations of solute. Non-linear sorption isotherms, which rapidly attain equilibrium in the chromatographic transit time, can also be evaluated by inverse chromatography.
The period of the detector response before elution and after passage of a non-sorbed pulse, such as air, is referred to as the prepeak period. The area of the detector response during this prepeak period is proportional to the sorption at a pressure equivalent to a specific response height provided that there are no appreciable non-linear kinetic factors restricting elution. The response height is determined by the desorption phase. The prepeak time to any specific solute concentration in the gas phase is determined by the sorption phase.
Integrating detector response over the elution concentration profile provides prepeak and peak areas proportional to sorption and desorption only if there is a linear response of the detector to solute mass, and equilibrium is reversible and achieved in solute transit.
Differences in the proportionality constants between areas and heights for mass injected will produce corresponding discrepancies in the calculation of sorption isotherms. Such discrepancies result from the existence of nonlinear concentration relationships with hysteresis (nonequilibrium conditions) for cycles of sorption and desorption.
In conventional inverse chromatography, only the amount of effluent solute leaving the stationary phase is monitored. Incomplete elution of the solute from the stationary phase results in underestimation of both prepeak and peak area as well as partial solute pressure. The relation between height of the peak and vapor pressure, if not linear because of incomplete elution of solute, can be seriously in error at low pressure when calculated from linear calibration data. These errors tend to linearize sorption isotherms that are non-linear when determined by long term gravimetric studies.
The linear transport of a solute in the mobile gas phase isothermally through a column containing a stationary phase is characterized by a number of changes in the solute concentration created by diverse factors. First, there is a partition coefficient between the mobile and stationary phases which may vary from a simple concentration independent constant to a very complex, concentration dependent constant. Second, the relationship can be modified by kinetic effects. These effects include peak broadening as a result of solute diffusion in the stationary phase as well as in the void volume or carrier gas phase. This broadening is particularly significant when solid stationary phases are used as opposed to liquid or coated substrates.
In conventional chromatography, a relatively small mass of solute is injected as a sharp pulse into a large mass of solid phase in a long column. The pulse rapidly shifts from a sharp square wave shape into a Gaussian shape. The peak position and height are governed by thermodynamic interactions between the solute and substrate and the peak width is governed by diffusional effects. Selection of substrate and solute concentration, temperature and flow rate can often be achieved to obtain a relatively narrow band maximizing the thermodynamic parameters and minimizing diffusional ones.
One approach to the problem of non-ideal or non-equilibrium conditions is to use a post elution pulse of appropriately elevated temperature to elute the strongly bound solute as a peak area instead of as a diffuse non-quantifiable rear boundary at a lower temperature. Paik, S. W. and Gilbert, S. G., Water Sorption Isotherms of Sucrose and Starch by Modified Inverse Frontal Gas Chromatography, J. of Chromatogr. 351 (3), 417-423 (1986).
Thus, the modified frontal inverse chromatography desorption method provides satisfactory agreement with static or long term equilibrium studies but requires a series of maintained solute concentrations to cover the full sorption isotherm range. The advantages of rapidity and simplicity in pulse or elution chromatography method are hence not present.
Accordingly, there have been significant needs for improvements in methods and in the apparatus for determining sorption isotherms of food by inverse chromatography.